QQ-plots: Quantile-Quantile plots - R Base Graphs - Easy Guides - Wiki (2024)

FAQs

What is QQ quantile-quantile plots? ›

The quantile-quantile (q-q) plot is a graphical technique for determining if two data sets come from populations with a common distribution. A q-q plot is a plot of the quantiles of the first data set against the quantiles of the second data set.

QQ plots can be made in R using a function called qqnorm(). Simply give the vector of data as input and it will draw a QQ plot for you. (qqline() will draw a line through that Q-Q plot to make the linear relationship easier to see.)

Examining data distributions using QQ plots

Points on the Normal QQ plot provide an indication of univariate normality of the dataset. If the data is normally distributed, the points will fall on the 45-degree reference line. If the data is not normally distributed, the points will deviate from the reference line.

Q–Q plots can also be used as a graphical means of estimating parameters in a location-scale family of distributions. A Q–Q plot is used to compare the shapes of distributions, providing a graphical view of how properties such as location, scale, and skewness are similar or different in the two distributions.

Quantiles are values that split sorted data or a probability distribution into equal parts. In general terms, a q-quantile divides sorted data into q parts. The most commonly used quantiles have special names: Quartiles (4-quantiles): Three quartiles split the data into four parts.

QQ plot (or quantile-quantile plot) draws the correlation between a given sample and the normal distribution. A 45-degree reference line is also plotted. QQ plots are used to visually check the normality of the data.

To draw a Quantile-Quantile (Q-Q) plot, you can follow these steps: Collect the Data: Gather the dataset for which you want to create the Q-Q plot. Ensure that the data are numerical and represent a random sample from the population of interest. Sort the Data: Arrange the data in either ascending or descending order.

quantile returns estimates of underlying distribution quantiles based on one or two order statistics from the supplied elements in x at probabilities in probs .

Q-Q plots are used to find the type of distribution for a random variable whether it be a Gaussian distribution, uniform distribution, exponential distribution or even a Pareto distribution. You can tell the type of distribution using the power of the Q-Q plot just by looking at it.

A P-P plot compares the empirical cumulative distribution function of a data set with a specified theoretical cumulative distribution function F(·). A Q-Q plot compares the quantiles of a data distribution with the quantiles of a standardized theoretical distribution from a specified family of distributions.

What is a Q-Q plot with two samples? ›

Alternatively, a q-q plot assesses whether two sets of sample data come from the same distribution. A q-q plot orders the sample data values from smallest to largest, then plots these values against the expected value for the specified distribution at each quantile in the sample data.

A Q-Q (quantile-quantile) plot shows how two distributions' quantiles line up, with our theoretical distribution (e.g., the normal distribution) as the x variable and our model residuals as the y variable.

To search for evidence of systematic bias (from unrecognized population structure, analytical approach, genotyping artifacts, etc.), a quantile-quantile (Q-Q) plot can be used to characterize the extent to which the observed distribution of the test statistic follows the expected (null) distribution.

A Q-Q (Quantile-Quantile) plot is another graphic method for testing whether a dataset follows a given distribution. It differs from the probability plot in that it shows observed and expected values instead of percentages on the X and Y axes.

A chi square quantile-quantile plots show the relationship between data-based values which should be distributed as χ2 and corresponding quantiles from the χ2 distribution.